Binary outcomes break least squares (predictions outside [0, 1], heteroskedastic errors by construction). Logit and Probit model the probability through a link function and are fitted by iteratively reweighted least squares — Newton's method on the likelihood, which is why it converges in a handful of steps.
Reported alongside the coefficients: the likelihood-ratio test against an intercept-only model, AIC/BIC, and marginal effects — the average derivative of the probability (AME) and the derivative at the average covariate (MEM). Coefficients are on the log-odds scale; marginal effects are on the probability scale, which is usually what a reader wants.
Standard errors use the expected information matrix, the convention of statsmodels' GLM family. A fit that fails to converge usually signals perfect separation — one combination of regressors predicts the outcome exactly — which is a data problem, not a numerical one.
Frequently asked questions
Logit or Probit?
Statistically they rarely disagree in practice; logit's coefficients read as log-odds and its odds ratios are easy to exponentiate. Probit implies normal errors, which matters when the model feeds a simulation.
Why trust AME over the coefficient?
A logit coefficient of 0.8 does not mean "80% more likely". The probability change per unit of x depends on where you stand — AME averages that over the sample, which is the honest summary.
中文说明
二分类结果会破坏最小二乘（预测越出 [0, 1]、误差天然异方差）。Logit 与 Probit 通过连接函数刻画概率，用迭代重加权最小二乘拟合——即似然上的牛顿法，因此几步就收敛。
系数之外还报告：对仅截距模型的似然比检验、AIC/BIC，以及边际效应——概率的平均导数（AME）与平均协变量处的导数（MEM）。系数在对数发生比尺度；边际效应在概率尺度，通常才是读者要的数。
标准误采用期望信息矩阵（statsmodels 的 GLM 家族惯例）。拟合不收敛通常意味着完全分离——某个自变量组合完美预测了结果——这是数据问题，不是数值问题。
常见问题
选 Logit 还是 Probit？
实践中两者结论很少分歧；logit 系数可读作对数发生比、取幂即得发生率比。若模型要接入模拟且误差需正态，则用 probit。
为什么看 AME 而不是系数？
logit 系数 0.8 不等于“可能性高 80%”。x 每单位的概率变化取决于所处位置——AME 在样本上取平均，是诚实的摘要。